Numerical evaluation of eigenvalues of the sheet diffusion problem in the surface/diffusion mixed regime

in relaxation experiments where both bulk diffusion and surface processes a re rate controlling, the theoretical transient depends on the roots beta (n ) of the transcendental equation beta (n) tan beta (n) = L, in which L cont ains the surface rate constant, the diffusion constant and sample dimension s. A method is presented to numerically evaluate the roots beta (n) to high precision, which is necessary in the evaluation of the surface and bulk tr ansport parameters through curve fitting. The method is simple, fast and ac curate. It is demonstrated that large errors in these parameters can occur if the roots are not evaluated to high precision. (C) 2000 Elsevier Science B.V. All rights reserved.